Instruction: Describe advanced feature engineering techniques in R and their impact on machine learning model performance.
Context: This question assesses the candidate's ability to enhance machine learning models through sophisticated feature engineering methods in R.
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Firstly, one advanced technique I frequently employ in R is the creation of interaction features. Interaction features are derived from existing data features and can provide a model with richer insights about the underlying patterns. For instance, if working on a housing price prediction model, multiplying the number of bedrooms by the number of bathrooms to create an 'interaction' feature can capture a dimension of housing luxury that individual features might not. In R, this can be efficiently done using the interaction() function, or through manual feature creation.
Another technique is polynomial feature expansion, which involves creating polynomial features from the existing variables. This method can help in capturing non-linear relationships between the variables...